Raster scan and single-pixel imaging at visible (VIS) range

The spectral domain between microwaves and infrared is called Terahertz, and the electromagnetic waves specific to this domain oscillate at frequencies between 0.1 - 30 THz. Although considerable progress has been made in the development of sources and detectors, the most accessible data recording/measurement technique for this spectral domain is, for now, single pixel detection.

Raster scanning is one method to achieve detection with a single pixel detector. This involves scanning the object pixel by pixel and reconstructing it using computational methods. The first stage involves design/simulation activities to identify an optimal single-pixel imaging setup. It is also taken into account that eventually the experimental setup will have to incorporate a scanning interferometer with spectroscopy and profilometry functions.

Several CAD simulations of single-pixel optical imaging setups were performed, including a tentative interferometric setup. Given that THz radiation is invisible we performed initial designs/ testing in the visible spectral range, both coherent and broadband/LED radiation. The development of the automation and control system (including the control of the translation tables and the acquisition of the signal from the photodetector) could only be carried out and tested in a visible radiation setup; otherwise, it is not feasible because a working experimental model is needed. Besides, the alignment of some experimental configurations as well as the testing of some concepts is achieved in a much shorter time by initially working with visible radiation. The transition to a THz radiation setup can be easily implemented at a later stage.

Single-pixel imaging by raster scanning method on an experimental model with coherent radiation from a HeNe laser (λ = 632.8 nm) was tested. At this point, the acquisition was performed by continuous scanning and recordings at constant time intervals. We tested various optical components, scanning speeds and resolutions to determine the optimal conditions for obtaining images of specially designed transmissive samples. Resolutions of 1024px², 4096px² and 16384px², respectively, were achieved.

Single-pixel imaging at terahertz (THz) range

After the imaging results obtained for VIS radiation, the ones with terahertz (THz) radiation are presented here. The main differences in the experimental setup are the optical components, the radation source and the detector, as they cover the THz range. The images below are acquired with broadband radiation in the 20 - 30 THz spectral region, since the source emmitts a black body radiation at 1200 K (550 nm - 15 μm or 20 - 545 THz) and the single-pixel detector measures in the range 0.1 - 30 THz. The images appear slightly blurry due to the broadband imaging.

Scanning interferometry

The term scanning interferometry means that localization of interference fringes during scanning of the optical path length (OPL) provides a way of measurement by controlled manipulation of the phase difference or optical path difference (OPD). Applications such as spectroscopy or profilometry are achieved by scanning of the interferogram or of the coherence of the input source, respectively. In this project, we designed and implemented both a visible and a terahertz experimental setup to measure the spectrum of the incident radiation or the profile of specific objects. These experimental arrangements are presented below. Depending on the measurement, the scanning is achieved by rotation of both mirrors around their point of intersection at a right angle or by translating one of the mirrors from the position of zero path difference (ZPD).

Development of functions - Fourier transform spectroscopy (FTS)

Fourier transform spectroscopy (FTS) is one application that involves scanning interferometry and single-pixel detection. The measurements imply scanning and recording the interferogram of the investigated source and, by Fourier transformation, extracting its spectrum. Depending on the necessary spectral resolution a number of 512, 1024, 2048, 4096, 8192, etc. should be acquired.

For this development function two black body radiation sources were used, namely a stabilized nitride globar ligh source (550 nm - 15 μm) from Thorlabs and the ARCLIGHT-MIR broadband lamp (1 - 25 μm) from Arcoptix. The spectra of these two sources are depicted bellow, together with the interest spectral range: 10 - 15 μm (20 - 30 THz).

Bellow are a series of Haidinger interference systems, computed for two broadband sources, one emmitting in the range 10 - 15 μm (20 - 30 THz) and the other in the range 10 - 25 μm (12 - 30 THz), respectively. They are measured from 512, 2048 or 4096 data points, a distance d = 2.6 μm between the two interfering sources and using an imaging lens with f = 50 mm.

Practically, the interferogram data is acquired with a single-pixel detector by scanning it in front of the detector via translation of the interferometer mirror. Thus, there will be an optical path difference (OPD) accumulation as a function of the intensity distribution that is recorded. The spectrum of the radiation source is obtained by applying the Fourier transformation to this recorded interferogram. Bellow are some examples in the interest spectral range for various number of data points. Note that the greater the number of data points the greater the OPD and the spectral resolution.

Development of functions - phase-shifting interferometry (PSI)

The second function that was developed within this project is phase-shifting interferometry (PSI) at THz frequencies. This implies changing the phase difference between the two interfering waves in a controlled manner by altering the distance between the two mirrors. Therefore, a scanning of the interferogram is also achieved. While in FTS the scanning is realized in very small steps, in PSI they are considerably larger. Also, the number of steps is, depending on the method used, much smaller in the case of PSI than FTS. The application developed with PSI is optical profilometry.

Using the 4-step phase-shifting interferometry method, the following computations were performed: the four phase-shifted Haidinger interference systems, wrapped phase, unwrapped phase, 3D profile and 2D profile. These simulations assume two plane mirrors in the interferometer (i.e., no object) and the following parameters: wavelength of 10.6μm, a distance of 2mm between sources and an imaging lens with the focal distance of 50mm.

The results for the same simulations as above are presented below but using a reflective object instead of the second mirror.

The same computations were performed using the 4-step method described above, but with straight equispaced interference fringes. This fringes are obtained by tilting one mirror at an angle around the vertical axis; this being a more reliable approach in profilometry measurements, given that straight and not curved surfaces are analyzed. These simulations assume a plane mirror and a reflective object in the interferometer; the following parameters were also used: wavelength of 10.6μm, 0.015 mrad angle between mirrors and an imaging lens with the focal distance of 50mm.

The results for 0.06 mrad angle between mirrors are presented below.

Following is another set of simulations using straight fringes with object and the following conditions: wavelength of 12μm and 0.02mrad angle between mirrors and an imaging lens with the focal distance of 50mm.

Below is another set of simulations using straight fringes with object and the following conditions: wavelength of 15μm and 0.06mrad angle between mirrors and an imaging lens with the focal distance of 50mm.